Distance alert systems, in particular for assisting parking into a parking space, are known, in which the distance to obstacles in the vehicle's surroundings is measured and in which the driver is alerted of such obstacles via corresponding displays and/or acoustic signals. It should be taken into account in these alerts that a driver must still respond to the alert, i.e., an alert must be output relatively early in order to be able to safely prevent a collision. Error tolerances of the sensors must also be taken into account. This tends to result in the fact that more alerts are output than are actually needed by the driver. In particular when performing parallel parking maneuvers or when passing through bottlenecks it may be the case that the vehicle corners come very close to objects and the distance is less than an alert distance for which an alert is triggered. Since the alert intensity generally increases with a decreasing distance, a particularly noticeable alert is output at these very small distances, e.g., an acoustic continuous tone. Although an alert is output, a collision is not to be expected due to the vehicle's travel path. Therefore, an unnecessary alert is output to the driver.